On a q-analogue of the multiple gamma functions

A $q$-analogue of the multiple gamma functions is introduced, and is shown to satisfy the generalized Bohr-Morellup theorem. Furthermore we give some expressions of these function.Comment: 8 pages, AMS-Late

Optimising Trade-offs Among Stakeholders in Ad Auctions

We examine trade-offs among stakeholders in ad auctions. Our metrics are the revenue for the utility of the auctioneer, the number of clicks for the utility of the users and the welfare for the utility of the advertisers. We show how to optimize linear combinations of the stakeholder utilities, showing that these can be tackled through a GSP auction with a per-click reserve price. We then examine constrained optimization of stakeholder utilities. We use simulations and analysis of real-world sponsored search auction data to demonstrate the feasible trade-offs, examining the effect of changing the allowed number of ads on the utilities of the stakeholders. We investigate both short term effects, when the players do not have the time to modify their behavior, and long term equilibrium conditions. Finally, we examine a combinatorially richer constrained optimization problem, where there are several possible allowed configurations (templates) of ad formats. This model captures richer ad formats, which allow using the available screen real estate in various ways. We show that two natural generalizations of the GSP auction rules to this domain are poorly behaved, resulting in not having a symmetric Nash equilibrium or having one with poor welfare. We also provide positive results for restricted cases.Comment: 18 pages, 10 figures, ACM Conference on Economics and Computation 201

Observation of Bell Inequality violation in B mesons

A pair of $B^0\bar B^0$ mesons from $\Upsilon(4S)$ decay exhibit EPR type non-local particle-antiparticle (flavor) correlation. It is possible to write down Bell Inequality (in the CHSH form: $S\le2$) to test the non-locality assumption of EPR. Using semileptonic $B^0$ decays of $\Upsilon(4S)$ at Belle experiment, a clear violation of Bell Inequality in particle-antiparticle correlation is observed: S=2.725+-0.167(stat)+-0.092(syst)Comment: Conference Proceeding for Garda Lake Workshop 2003 "Mysteries, Puzzles and Paradoxes in Quantum Mechanics

Congruence schemes

A new category of algebro-geometric objects is defined. This construction is a vast generalization of existing F1-theories, as it contains the the theory of monoid schemes on the one hand and classical algebraic theory, e.g. Grothendieck schemes, on the the other. It also gives a handy description of Berkovich subdomains and thus contains Berkovich's approach to abstract skeletons. Further it complements the theory of monoid schemes in view of number theoretic applications as congruence schemes encode number theoretical information as opposed to combinatorial data which are seen by monoid schemes

Suppressive activity of a macrolide antibiotic, roxithromycin on co-stimulatory molecule expression on mouse splenocytes in vivo.

The influence of roxithromycin (RXM) on the expression of co-stimulatory molecules, CD40, CD80 and CD86, was examined in vivo. When BALB/c mice were immunized intraperitoneally with two doses of dinitrophenylated ovalbumin (DNP-OVA) at 1 week intervals, intraperitoneal administration of RXM at 250 microg/kg once a day for 14 days strongly suppressed IgE contents in sera obtained from mice 22 days after the first immunization. In addition, RXM treatment of mice suppressed endogenous IL-4 contents in aqueous spleen extracts, which were enhanced by DNP-OVA immunization. We next examined the influence of RXM on co-stimulatory molecule expression on splenic lymphocytes. RXM treatment of the immunized mice caused suppression of CD40 expression, but this treatment did not affect CD80 and CD86 expression